Karsten E. Thompson

Coupling pore-scale networks to continuum-scale models of porous media

Network modeling is a useful tool for investigating pore-scale behavior and in some cases for determining macroscopic information such as permeability, relative permeability, and capillary pressure. Physically representative network models are particularly useful because quantitative and predictive results can be obtained. In the past, network models have been used as stand-alone tools for predicting flow behavior at the pore scale. In these cases, simple boundary conditions such as a pressure gradient in one direction are generally imposed on the network. However, with the increasing emphasis on multiscale modeling techniques, the real potential of network models is as a bridge from the pore to the continuum scale. In this context, continuum-scale and pore-scale models are used jointly; pore-scale behavior is upscaled and substituted into a continuum-scale simulator. Methods for integrating these techniques are being developed, and one important question is how to match boundary conditions for the two scales. In this work, physically representative network models created from computer-generated sphere packings are coupled to adjacent continuum-scale models. By coupling the two regions, realistic boundary conditions are enforced, which reflect the heterogeneity of the packed bed as well as the resistance of the adjacent medium. Results of the direct coupling show that both pore-scale phenomena and macroscopic behavior (such as flowrate) are significantly different than when these same parameters are obtained by implementing simple (decoupled) boundary conditions.

Theory, modeling and experiment in reactive transport in porous media

Abstract We review selected recent developments in reactive flow and transport in porous media, with emphasis on strongly coupled flows, interphase mass transfer, solute transport via dispersion and adsorption and modeling. On the one hand, modeling, theory and experiment continue to provide useful insights into the behavior of natural and engineered systems. On the other hand, real systems continue to reveal instances of non-classical behavior that is not explainable by traditional approaches. This is the sign of a healthy area of science, but it is accompanied by certain challenges. In some applications, it establishes the necessity of multiscale modeling, in particular upscaling from the pore level, though predictive work is especially difficult at that scale. In other applications, however, the central question may be not how to model a particular system, but whether it can be modeled in a meaningful way. Continued progress will require renewed focus on elements of the scientific method: testable predictions, crucial experiments and falsification of hypotheses (Popper K. All life is problem-solving, Routledge, London, 1999•).

Experimental analysis of local mass transfer in packed beds

Abstract The mass transfer behavior from single spheres within random packings was examined in order to quantify the effects of local structure and hydrodynamics on mass transfer. Results show that in the sphere packs studied, structural differences at the pore scale cause the local Peclet number to vary by more than an order of magnitude and the exponent in the Sherwood versus Peclet number relationship to vary between approximately 0.3 and 0.7, both as a function of location within the packing. These combined effects cause at least a two-fold variation in local mass transfer rates and significant differences in the sensitivity of local mass transfer rates to changes in the overall flowrate to the bed. Two distributed parameters are introduced to quantify these effects, which collapse mass transfer data onto a single curve relating the local Sherwood number to a local Peclet number. The physical significance of these parameters is discussed, which aids in our understanding of fundamental behavior in disordered systems. Finally, we show how this information is used to calculate a spatially averaged mass transfer coefficient for dispersed interfaces under conditions where the total mass transfer rate for these interfaces does not reflect average behavior for the bed.

Numerical modeling of reactive polymer flow in porous media

Abstract This paper presents a new numerical model of reactive polymer flow in heterogeneous porous media. A moment representation of the log–normal polymer molecular weight distribution is used to model polymer as a multi-component species. Three leading moments are used to simulate the polymer transport and reaction processes in a two-dimensional porous medium. The 2D, multi-phase polymer flow model is based on a mass-transport equation for multi-component species and is coupled with kinetic models of the gelation process using an operator splitting scheme. The sensitivity of various parameters and constitutive equations is presented.

Influence of computational domain boundaries on internal structure in low-porosity sphere packings

Collective rearrangement is an important class of algorithms for the computer generation of random sphere packings, especially for those of low porosity. In this paper we examine how the choice of boundary conditions affects internal packing structure. The results help to quantify the depth to which non-periodic boundaries influence internal structure. More interesting results are obtained for periodic boundary conditions, showing that for small packings, self-assembly into ordered packings is possible, even without a seed structure or undue influence from the algorithm. Furthermore, the structure depends on the shape of the periodic domain. Finally, we propose examining the transition from random to ordered packings to better characterize the random-close-packed (RCP) limit and its associated packing structures.

Physical Pore Properties and Grain Interactions of SAX04 Sands

During the 2004 Sediment Acoustic eXperiment (SAX04), values of sediment pore properties in a littoral sand deposit were determined from diver-collected cores using traditional methods and image analysis on X-ray microfocus computed tomography (XMCT) images. Geoacoustically relevant pore-space properties of sediment porosity, permeability, and tortuosity were evaluated at scales ranging from the pore scale to the core scale from “mud-free” sediments collected within the 0.07-km² study area. Porosity was determined from water-weight-loss measurements to range from 0.367 to 0.369, from 2-D image analysis to range from 0.392 to 0.436 and from 3-D image analysis to range from 0.386 to 0.427. The range of permeability from all measurements was 2.8 × 10^-11 m² to 19.0 × 10^-11 m², however the range of permeability within each technique was much narrower. Permeability was determined using a constant head (CH) apparatus (<i>k</i>_range = 2.88 to 3.74 × 10^-11 m²), from a variant of the Kozeny-Carman (KC) equation (<i>k</i>_range = 12.4 to 19.0 × 10^-11 m²), from an effective medium theory technique (<i>k</i>_range = 5.60 to 13.3 × 10^-11 m²) and from a network model (<i>k</i>_range = 8.49 to 19.0 × 10^-11 m² ). Permeability was determined to be slightly higher in the horizontal than in the vertical direction from the network model. Tortuosity ranged from 1.33 to 1.34. Based upon the small coefficients of variation for the conventionally determined pore-space properties, the sand sediment within these core samples was deemed homogeneous at all of the SAX04 sites. Additionally, grain interactions, specifically grain coordination number and grain contact areas, were determined from XMCT images. Grain contacts ranged in size from small point contacts of 136 μm² to large-area contacts the size of grain faces ( >4500 × μm²). The mean coordination number was similar to that of a cubic packing (six), but sometimes exceeded 12, which is the coordination number for a hexagonal close packing of spheres.

Investigating the correlation between residual nonwetting phase liquids and pore-scale geometry and topology using synchrotron x-ray tomography

The entrapment of nonwetting phase fluids in unconsolidated porous media systems is strongly dependent on the pore-scale geometry and topology. Synchrotron X-ray tomography allows us to nondestructively obtain high-resolution (on the order of 1-10 micron), three-dimensional images of multiphase porous media systems. Over the past year, a number of multiphase porous media systems have been imaged using the synchrotron X-ray tomography station at the GeoSoilEnviroCARS beamline at the Advanced Photon Source. For each of these systems, we are able to: (1) obtain the physically-representative network structure of the void space including the pore body and throat distribution, coordination number, and aspect ratio; (2) characterize the individual nonwetting phase blobs/ganglia (e.g., volume, sphericity, orientation, surface area); and (3) correlate the porous media and fluid properties. The images, data, and network structure obtained from these experiments provide us with a better understanding of the processes and phenomena associated with the entrapment of nonwetting phase fluids. Results from these experiments will also be extremely useful for researchers interested in interphase mass transfer and those utilizing network models to study the flow of multiphase fluids in porous media systems.

Numerical analysis of the effects of local hydrodynamics on mass transfer in heterogeneous porous media

Many engineering problems require the estimation of mass transfer coefficients in porous materials. In heterogeneous materials or in cases where mass transfer sites are not spatially uniform, empirical equations for mass transfer coefficients vary widely, and the origin of these differences is not well understood. In this article, we use a stochastic algorithm to model mass transfer from single particles in a two-dimensional heterogeneous packed bed. The computed mass transfer coefficients are used to generate a distribution of local Peclet numbers in the bed. Detailed hydrodynamics are then used to interpret variations in the local Peclet number. The results show clear relationships between pore structure, streamline patterns, and mass transfer rates.

Fabrication of 2.5D Rock-Based Micromodels With High Resolution Features

Fabrication of 2.5D rock-based micromodels with high resolution features is presented using SU-8 multi-layer lithography and nickel electroforming for nickel molds. Processes associated with SU-8 were carefully optimized by the use of the vacuum contact, the use of UV filter, and controls of UV exposure doses and baking times. The use of SU-8 MicroSpray enabled the easy fabrication of multi-layers of SU-8, while exhibiting some total thickness variations. The thirteen layered SU-8 samples showed reliable patterning results for features at 10 and 25 μm resolutions, and minor pattern distortions of features at the 5 μm resolution. Flycutting method employed in multi-layer lithography of SU-8 yielded accurate total thickness control within ±1.5 μm and excellent pattern formation for all of 5, 10, and 25 μm features. Electroforming of nickel was optimized with electroplating bath composition and electroplating parameters such as current density to realize the high resolution nickel mold. The fabricated nickel molds from flycutting based SU-8 samples revealed the feasibility of manufacturing the minimum features down to 5 μm for thirteen layers without any pattern distortions. The replication-based micromolding method will allow for fabrication of micromodels in a variety of materials such as polymers and ceramics. The high resolution, 2.5D micromodels will be used for investigation of pore-scale fluid transport, which will aid in understanding the complicated fluidic phenomena occurring in the 3D reservoir rock.Copyright

Flow Visualization in Artificial Porous Media From Microfluidic PMMA Devices

Microfluidic polymethylmethacrylate (PMMA) devices for study of particle transport in artificial porous media were designed and microfabricated using hot embossing with a brass mold insert containing a microchannel network with eight layers. After thermal bonding to enclose the microchannel network, a process protocol was applied to successfully remove bubbles in the PMMA device. Characterization protocols were developed for study of fluorescent particle tracking, accumulation, and retention in these microfluidic chip artificial porous media. Particle accumulation and retention was observed throughout the microfluidic network domain and predominantly at the inlet section of the PMMA device due to entrance effects. Particle Image Velocimetry of the PMMA device allowed for generating velocity profiles in the chip microchannel networks.Copyright